MAA-AWM Etta Z. Falconer Lecture

What can mathematics tell us about the treatment of cancer? Cancer is a myriad of individual diseases, with the common feature that an individual's own cells have become malignant.  It is believed that a healthy individual keeps potentially cancerous cells from developing into a threatening tumor through a complicated network of immune response and mechanisms built into the cell cycle that recognize aberrant cells and control their proliferation. Thus, the treatment of cancer poses great challenges, since an attack must be mounted against cells that are nearly identical to normal cells.  Mathematical models that describe tumor growth in tissue, the immune response, and the administration of different therapies can suggest treatment strategies that optimize treatment efficacy and minimize negative side effects. However, the inherent complexity of the immune system and the spatial heterogeneity of human tissue gives rise to mathematical models that pose unique analytical and numerical challenges. These include modeling behavior over vastly different time scales, incorporating delays into the model, optimization in high-dimensional spaces, and fitting large sets of dependent parameters to data.


In this talk I will present an overview of work that I have done in this area, with the help of many collaborators, over the last ten years, highlighting the various approaches we have taken to tackle these mathematical challenges.

Biography: A California native, Ami Radunskaya received her Ph.D. in Mathematics from Stanford University in 1992 after graduating with honors from the University of California at Berkeley. She has been on the faculty at Pomona College in Claremont, California for 15 years. Knowing that mathematics is both fun and useful, she has committed herself to increasing the participation of women and under-represented groups in the mathematical sciences. She has been a faculty member of the Summer Scholar’s Program, an outreach program for talented high school students, and has been a faculty member and occasional local director of the EDGE (Enhancing Diversity in Graduate Education) program for over ten years.

Professor Radunskaya's research is in ergodic theory, dynamical systems, and applications to various "real-world" problems. Some current research projects involve mathematical models of cancer immuno-therapy, a collaboration with the electrical company modeling large clusters of windmills, and, on the more theoretical side, delay equations and the analysis of stochastic perturbations of dynamical systems. Her first career as a professional 'cellist has also led to work at the interface of mathematics and music, including `technoclectic' compositions for live performers accompanied by dynamical systems.

Professor Radunskaya was awarded an Irvine Fellowship for Excellence in Faculty Mentoring in 2004.